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Zbl 1012.35076
Liu, Zhengrong; Yang, Chenxi
The application of bifurcation method to a higher-order KdV equation.
(English)
[J] J. Math. Anal. Appl. 275, No.1, 1-12 (2002). ISSN 0022-247X

Summary: Bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the higher-order KdV equation $$u_t+au^nu_x +u_{xxx}=0,$$ where $n\ge 1$ and $a\in\bbfR$. Numbers of solitary waves are given for each parameter condition. Under some parameter conditions, explicit solitary wave solutions are obtained. Specially, some new solitary wave solutions are found for the KdV or MKDV equation.
MSC 2000:
*35Q53 KdV-like equations
37K50 Bifurcation problems
37K40 Soliton theory, asymptotic behavior of solutions

Keywords: bifurcation of solitary waves; higher-order KdV equation; explicit solitary wave solutions; MKDV equation

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